Question: Rewrite as a simplified fraction. ${1.39\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1393.3333...\\ 100x &= 139.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1254}$ ${x = \dfrac{1254}{900}} $ ${x = \dfrac{209}{150}} \text{or} {1 \dfrac{59}{150}}$